Quantifying the Influence of Covalent Metal‐Ligand Bonding on Differing Reactivity of Trivalent Uranium and Lanthanide Complexes

Abstract Qualitative differences in the reactivity of trivalent lanthanide and actinide complexes have long been attributed to differences in covalent metal‐ligand bonding, but there are few examples where thermodynamic aspects of this relationship have been quantified, especially with U3+ and in the absence of competing variables. Here we report a series of dimeric phosphinodiboranate complexes with trivalent f‐metals that show how shorter‐than‐expected U−B distances indicative of increased covalency give rise to measurable differences in solution deoligomerization reactivity when compared to isostructural complexes with similarly sized lanthanides. These results, which are in excellent agreement with supporting DFT and QTAIM calculations, afford rare experimental evidence concerning the measured effect of variations in metal‐ligand covalency on the reactivity of trivalent uranium and lanthanide complexes.


Synthesis and Characterization
General considerations. All reactions were carried out under an atmosphere of N2 or Ar using glovebox or standard Schlenk techniques. All glassware was heated at 150 °C for at least two hours and allowed to cool under vacuum before use. Solvents were dried and deoxygenated using a Pure Process Technologies Solvent Purification System and stored over 3 Å molecular sieves. Deuterated solvents were deoxygenated with five freeze-pump-thaw cycles and stored over 3 Å molecular sieves for at least 3 days before use. K(H3BP t Bu2BH3), U2(H3BP t Bu2BH3)6, and Nd2(H3BP t Bu2BH3)6 were prepared as previously reported. [1][2] LnI3 starting materials were used as received from Alfa Aesar or Strem Chemicals. 1 H NMR data were collected on a Bruker AVANCE-400 operating at 400 MHz, or a Bruker AVANCE-500 operating at 500 MHz. The 11 B NMR data were collected on a Bruker AVANCE-400 operating at 128 MHz or a Bruker AVANCE-500 operating at 160 MHz. 31  La2(H3BP t Bu2BH3)6. LaI3 (0.201 g, 0.387 mmol) and K(H3BP t Bu2BH3) (0.245 g, 1.16 mmol) were loaded into a 5 mL FTS ball mill jar with two 5 mm stainless steel balls along with several drops of Et2O. The jar was hermetically sealed, transferred to an FTS shaker mill, and S3 milled at 1600 rpm for 120 min. The jar was then transferred to a glovebox and opened to reveal a white residue. The contents were extracted into an 11-dram vial with 40 mL chlorobenzene and stirred for several hours. The suspension was filtered through a fine frit and evaporated to dryness under vacuum to reveal a white solid. Et2O containing a small amount of pentane was added and gently heated until all the contents dissolved into solution (ca. 35 mL) and stored at -30˚C overnight to afford colorless plates (21 mg  La(H3B t Bu2PBH3)3(thf)3. LaI3 (0.100 g, 0.192 mmol) and K(H3BP t Bu2BH3) (0.122 g, 0.576 mmol) were stirred overnight in 10 mL of chlorobenzene. The solution was filtered through a sintered glass funnel and solvent was evaporated under reduced pressure. The white residue was dissolved in the minimum amount of thf, layered with pentane, and left for two days at - 30   Pr2(H3BP t Bu2BH3)6. PrI3 (0.100 g, 0.192 mmol) and K(H3BP t Bu2BH3) (0.122 g, 0.576 mmol) were transferred to a 5 mL stainless steel FTS ball milling jar followed by two 5 mm stainless steel balls and several drops of Et2O. The reaction vessel was sealed, removed from the glovebox, and milled for 90 minutes at 1600 rpm. Once the milling process was complete, the S5 vessel was transferred to a glovebox where an opaque yellow/green paste was scraped from the jar and stirred in approximately 15 mL of Et2O for several minutes. The mixture was filtered through a fine frit and the filtrate was evaporated to dryness under vacuum. The solid was dissolved in pentane and filtered, and the filtrate was evaporated to dryness to reveal an oil. The oil was dissolved in thf and vapor diffused with pentane. After one week at room temperature, yellowish green plate-like crystals had formed and were recovered from the bottom of the vial (99.7 mg).
Evaporating the mother liquor to dryness and repeating the vapor diffusion process with thf and pentane yielded a second crop of crystals (10 mg  Sm2(H3B t Bu2PBH3)6. SmBr3 (0.100 g, 0.182 mmol) and K(H3BP t Bu2BH3) (0.1162 g, 0.5482 mmol) were added to a 5 mL FTS ball milling jar followed by two 5 mm stainless steel balls and several drops of Et2O. The reaction vessel was sealed, removed from the glovebox, and milled for 90 min at 1600 rpm. Once the milling process was complete, the vessel was transferred to a glovebox where the mixture was scraped from the jar and stirred in approximately 15 mL of

Thermodynamic Studies
To quantify the thermodynamic parameters ΔH, ΔS, and ΔG associated with the dimer/monomer equilibrium, variable-temperature quantitative NMR spectroscopy (VT qNMR) studies were conducted in triplicate for each M2(H3BP t Bu2BH3)6 complex with M = U, La, Ce, Pr, and Nd. Concentration of the C6D5H in C6D6 was determined by integration of an external standard of ferrocene with known concentration, and the C6D5H concentration was used to calculate absolute concentration of the dimer and monomer at each temperature. Ferrocene was purchased from Sigma Aldrich and sublimed 5 times before use as the external standard in qNMR studies, as described previously. 3 Acquisition of the 1 H qNMR external standards were carried out following known acquisition and processing procedures (temperature, flip angle, acquisition time, spectral width, and relaxation) described by Napolitano et al. 3 Figure S1). S8 Figure S1. Overlay of the VT 1 H NMR spectra for the downfield monomer and dimer BH3 resonances of Ce(H3BP t Bu2BH3)3 from 300 K to 345 K and back to 300 K.
Van't Hoff plots were used to quantify the enthalpy (ΔH) and entropy (ΔS) with the deoligomerization of each dimer over the given temperature range ( Figure S2 -S6). 5-6 A linear regression of ln Keq vs 1/T was used to generate a line to give the slope and intercept containing ΔH and ΔS, respectively (Eq 1). These values were then used to obtain ΔG according to Eq 2.
Two methods were used to obtain the values of ΔH and ΔS and evaluate their uncertainties.
In the first method, each run of each triplicate data set was plotted to obtain ΔH and ΔS values that were then averaged to obtain standard deviations for comparison ( Figures S2 -S6). These values, which are provided in Table S2, are the average values and standard deviations provided in the main text.

S12
The second method used is the error propagation method described by Xue and coworkers, as shown in Eqs 3 and 4. [7][8][9] The drawback of this method is that it is known to give relatively large uncertainties in the values of ΔH and ΔS when the temperature range of the data collection (ΔT) is limited because of ΔT 2 and ΔT 4 in the denominator of both equations. This is true of the data described in this report; the equilibrium data could only be collected over a relatively short temperature range (ΔT = 45 K) because of the limited solubility of the complexes in cooled solutions and concerns about the reduced stability of the complexes at higher temperatures. We view the uncertainties obtained using this method as beingly overly conservative given the relatively high reproducibility of the data, as shown in Table S2. This is especially true with respect to the slope of the linear regressions where ΔH is derived. Nevertheless, we wish to provide the uncertainty analysis using Eqs 3 and 4 to show how the values compare.
Determining ΔH and ΔS using this second method requires plotting the natural log of the averaged Keq values obtained at each temperature vs. 1/T ( Figure S7). As expected, the ΔH and ΔS values obtained using this method are almost identical to those obtained using the first method (Tables S2 and S3). The uncertainties were then obtained using Eqs 3 and 4 and the following key variables. The uncertainty in temperature (σT/T) was 1 K. The average Keq and standard deviations (σKeq(ran)) determined at each temperature were used to calculate the random uncertainty (σKeq(ran)/Keq) in the data for that temperature. The largest random uncertainty obtained for each S13 data set was the value that was combined with the systematic uncertainty (σKeq(sys)/Keq), which is typically estimated at 5%, to obtain the total uncertainty σKeq/Keq according to Eq 5.
σKeq/Keq = [(σKeq(sys)/Keq) 2 + (σKeq(ran)/Keq) 2 ] 1/2 (5) complex. We repeated several additional VT runs and saw similar variability that did not improve the statistics on the y-intercept. Table S3. Average ΔH (kcal•mol -1 ) and ΔS (kcal•mol -1 •K -1 ) values obtained using the plot in Figure   S7 and the error propagation method of Xue and coworkers (Eqs 3 and 4). The  Table S2, especially considering that the consistency in the slopes of the lines where ΔH is determined. The uncertainties in ΔH for the other complexes are more reasonable at 0.7 -0.8 kcal•mol -1 and slightly larger than those obtained using the standard deviations due to the dependence on the small ΔT. The values used in Eqs. 3 and 4 and Figure S7 are provided in Table   S3 and S4 for comparison to the standard deviations in Table S2. S15  Olex2. 13 Publication figures were made using Mercury version 4.3.1 or Olex2. 13-14 S17 Figure S8. Molecular structure of Ce2(H3BP t Bu2BH3)6 with thermal ellipsoids at 50% probability.
Hydrogen atoms attached to carbon and co-crystallized pentane were omitted from the figure for clarity. Figure S9. Molecular structure of Pr2(H3BP t Bu2BH3)6 with thermal ellipsoids at 50% probability.

Metal
Some of the species have very small (<15 cm -1 ) imaginary modes associated with methyl rotations.
These did not impact the computed free energies because the quasiharmonic correction suggested by Cramer and Truhlar is used for all thermochemistry data in which normal modes less than 100 cm -1 are replaced with 100 cm -1 . 30 (Table S7-S11). Since the same trends emerge with all functionals, we include the TPSS-D3 results (and additional analysis at the same level) in the manuscript.

S22
DFT Results.   (Table S13). In the case of bridging ligands, the U-B distances were significantly shorter than for La, Ce, Pr, and Nd, which is in good agreement with those seen experimentally. The conformer search for La(H3BP t Bu2BH3)3 produced 18 conformers; each were optimized at the RI-TPSS-D3/def2-TZVP level of theory. All conformers and relative energies are reported (Table S12). M06-L results are in the subsequent tables.    The ratio of the absolute potential energy and Lagrangian kinetic energy (|V(r)|/G(r)) at bond critical point is the indicator of type of bonding. For pure closed shell interactions |V(r)|/G(r)) < 1 which indicate fully ionic or van der Waals interactions. For shared shell interaction |V(r)|/G(r) > 2 which is fully covalent. If the value of |V(r)|/G(r)) is between 1 and 2, that indicates partial covalency. We also report the bond degree (BD), defined as E(r)/ρ, that gives a measure of the degree of covalency in these bonds. More negative values of BD suggest a greater covalent interaction. [32][33][34] We obtained bond critical points for all chelating and bridging U-B and La-B bonds.

S25
However, for the Ce, Pr and Nd dimers, we did not find all BCPs despite searching from several S30 starting points (i.e., using the various options available in MultiWFN). The properties of individual BCPs are shown in Tables S19 -S23. The average values of these properties are given in Table   S18. The positive Laplacian at all BCPs indicates that these types of bonds are predominantly ionic; however, the negative energy density and the value of |V(r)|/G(r) falling in between 1 and 2 support that these bonds have some partial covalent character. The total electron density (ρ) at the chelating M-B bonds is lower in all lanthanides and uranium than the bridging ones. However, for the U-B bonds the electron density is higher than the lanthanides in both bridging and chelating ligands ( Figure 4, Figure S13). This indicates that U-B bonds have more covalent character than the lanthanides. This is also supported by the bond degree parameter which is more negative for U-B bonds.
Finally, we compute the delocalization index (δ), another tool to assess covalent contributions to bonding, that quantifies the number of electrons shared by the two atoms. The higher the value, the more covalent the bond. [35][36][37] In these complexes, the highest delocalization index was observed for U-B bonds in the bridging ligands supporting the conclusion of increased covalent character ( Figure S14, Table S24). In the lanthanide M-B bonds, the delocalization index is almost the same regardless of metal, which is consistent with bonding that does not change much across the series.